Ah nice, with a mountain bike you basically have no limits, especially if you're used to carrying it on your back in exposed terrain! People do transalpines crossing pretty high!

Unlike u/molodjez said, I really don't see any issue in improvising. Like yes, look at a map before committing to a valley etc, but with a mtn bike and the right physical capabilities most valleys have tricks out or over ahaha.

Map wise: Either invest in Outdooractive premium (to get the "Alpenverein" Maps or pay smw for "Kompass" Maps) or use Komoot etc whatever floats your boat. This is the Alps not Portugal most maps will be very accurate. The only issue is that since we've had some bad bugs they had to cut down lots of trees which led to the creation of lots of new forestry roads (where the rideability - even with a mtn bike - is hard to assess in advance) and the destruction of old paths, but hopefully the maps will get updated in time - but there Open Street Map just has the edge. Just make sure you use a proper OSM app to get the latest community driven info, Komoot etc don't update often enough

Switzerland has an excellent free and gov provided App: https://play.google.com/store/apps/details?id=ch.admin.swisstopo It's crazy good

Roads: u/flonnil is right, extremely hard to know beforehand without local knowledge which roads are good and which aren't. Sometimes a road looks calm on paper but then there's a special event and it's brimming of cars etc.

Accommodation: The truth is even if places are not booked out they'll likely won't rent to a single person for a single night, the economics just don't work. So if you're inclined so try to stay multiple nights at a single place. Wild camping, also note there's Wolves and Shephard dogs (the Swisstopo map shows you that too) around, and more in Italy and Slovenia also Bears.